Approximate expressions for the mean and the covariance of the maximum likelihood estimator for acoustic source localization

Acoustic source localization using multiple microphones can be formulated as a maximum likelihood estimation problem. The estimator is implicitly defined as the minimum of a certain objective function. As a result, we cannot get explicit expressions for the mean and the covariance of the estimator. We derive approximate expressions for the mean vector and covariance matrix of the estimator using Taylor´s series expansion of the implicitly defined estimator. The validity of our expressions is verified by Monte-Carlo simulations. We also study the performance of the estimator for different microphone array configurations.